Point is, the travel time from EMA to Solihull / Castle Bromwich would not be an obstacle to flying JLR line stop parts there rather than BHX, BHX is more convenient for sure, but if the differential between the costs of the two airport was that great then, believe me, they'd fly the stuff into EMA and truck it to the plants!
Don't think that the costs are that high at BHX, certainly not for parking, which for ad-hoc freighters that sit around waiting for their next job makes it very attractive.
The biggest attraction for BHX for ad-hoc cargo is the speedy handling of course, being on the Elmdon means that cargo can be offloaded straight off the aircraft into the truck and leave the airport 10 minutes after the aircraft has landed.
No warehouse charges either, which is a very large consideration for brokers and forwarders.
May explain why BHX handles ad-hoc cargo not only for JLR, but also GM, Bentley,BMW, and even Nissan, despite other aiports such as EMA, LPL, DSA, OXF, MME,NCL being so much closer to the eventual destination.